LMFDB - Embedded newform 8002.2.a.d.1.64

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.64
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.49694 q^{3} +1.00000 q^{4} +2.70604 q^{5} +2.49694 q^{6} -4.09546 q^{7} +1.00000 q^{8} +3.23472 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.49694 q^{3} +1.00000 q^{4} +2.70604 q^{5} +2.49694 q^{6} -4.09546 q^{7} +1.00000 q^{8} +3.23472 q^{9} +2.70604 q^{10} -3.05891 q^{11} +2.49694 q^{12} -5.82293 q^{13} -4.09546 q^{14} +6.75684 q^{15} +1.00000 q^{16} -2.91964 q^{17} +3.23472 q^{18} -6.16655 q^{19} +2.70604 q^{20} -10.2261 q^{21} -3.05891 q^{22} +3.22341 q^{23} +2.49694 q^{24} +2.32267 q^{25} -5.82293 q^{26} +0.586094 q^{27} -4.09546 q^{28} -2.85255 q^{29} +6.75684 q^{30} +1.43540 q^{31} +1.00000 q^{32} -7.63791 q^{33} -2.91964 q^{34} -11.0825 q^{35} +3.23472 q^{36} -0.878750 q^{37} -6.16655 q^{38} -14.5395 q^{39} +2.70604 q^{40} -5.55733 q^{41} -10.2261 q^{42} +3.80486 q^{43} -3.05891 q^{44} +8.75331 q^{45} +3.22341 q^{46} -11.9702 q^{47} +2.49694 q^{48} +9.77283 q^{49} +2.32267 q^{50} -7.29017 q^{51} -5.82293 q^{52} -12.5809 q^{53} +0.586094 q^{54} -8.27753 q^{55} -4.09546 q^{56} -15.3975 q^{57} -2.85255 q^{58} -0.694820 q^{59} +6.75684 q^{60} +4.49934 q^{61} +1.43540 q^{62} -13.2477 q^{63} +1.00000 q^{64} -15.7571 q^{65} -7.63791 q^{66} +6.20266 q^{67} -2.91964 q^{68} +8.04868 q^{69} -11.0825 q^{70} +7.73550 q^{71} +3.23472 q^{72} +11.7396 q^{73} -0.878750 q^{74} +5.79958 q^{75} -6.16655 q^{76} +12.5276 q^{77} -14.5395 q^{78} +12.5656 q^{79} +2.70604 q^{80} -8.24073 q^{81} -5.55733 q^{82} -6.89291 q^{83} -10.2261 q^{84} -7.90067 q^{85} +3.80486 q^{86} -7.12266 q^{87} -3.05891 q^{88} +9.00125 q^{89} +8.75331 q^{90} +23.8476 q^{91} +3.22341 q^{92} +3.58410 q^{93} -11.9702 q^{94} -16.6870 q^{95} +2.49694 q^{96} -8.71999 q^{97} +9.77283 q^{98} -9.89472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.49694	1.44161	0.720805	−	0.693138i	$-0.243772\pi$
$3$	2.49694	1.44161	0.720805	+	0.693138i	$0.243772\pi$
$4$	1.00000	0.500000
$5$	2.70604	1.21018	0.605090	−	0.796157i	$-0.293137\pi$
$5$	2.70604	1.21018	0.605090	+	0.796157i	$0.293137\pi$
$6$	2.49694	1.01937
$7$	−4.09546	−1.54794	−0.773970	−	0.633222i	$-0.781732\pi$
$7$	−4.09546	−1.54794	−0.773970	+	0.633222i	$0.781732\pi$
$8$	1.00000	0.353553
$9$	3.23472	1.07824
$10$	2.70604	0.855726
$11$	−3.05891	−0.922295	−0.461147	−	0.887324i	$-0.652562\pi$
$11$	−3.05891	−0.922295	−0.461147	+	0.887324i	$0.652562\pi$
$12$	2.49694	0.720805
$13$	−5.82293	−1.61499	−0.807495	−	0.589874i	$-0.799177\pi$
$13$	−5.82293	−1.61499	−0.807495	+	0.589874i	$0.799177\pi$
$14$	−4.09546	−1.09456
$15$	6.75684	1.74461
$16$	1.00000	0.250000
$17$	−2.91964	−0.708116	−0.354058	−	0.935223i	$-0.615199\pi$
$17$	−2.91964	−0.708116	−0.354058	+	0.935223i	$0.615199\pi$
$18$	3.23472	0.762432
$19$	−6.16655	−1.41470	−0.707352	−	0.706861i	$-0.750111\pi$
$19$	−6.16655	−1.41470	−0.707352	+	0.706861i	$0.750111\pi$
$20$	2.70604	0.605090
$21$	−10.2261	−2.23153
$22$	−3.05891	−0.652161
$23$	3.22341	0.672128	0.336064	−	0.941839i	$-0.390904\pi$
$23$	3.22341	0.672128	0.336064	+	0.941839i	$0.390904\pi$
$24$	2.49694	0.509686
$25$	2.32267	0.464534
$26$	−5.82293	−1.14197
$27$	0.586094	0.112794
$28$	−4.09546	−0.773970
$29$	−2.85255	−0.529705	−0.264853	−	0.964289i	$-0.585323\pi$
$29$	−2.85255	−0.529705	−0.264853	+	0.964289i	$0.585323\pi$
$30$	6.75684	1.23362
$31$	1.43540	0.257805	0.128902	−	0.991657i	$-0.458855\pi$
$31$	1.43540	0.257805	0.128902	+	0.991657i	$0.458855\pi$
$32$	1.00000	0.176777
$33$	−7.63791	−1.32959
$34$	−2.91964	−0.500714
$35$	−11.0825	−1.87329
$36$	3.23472	0.539121
$37$	−0.878750	−0.144466	−0.0722328	−	0.997388i	$-0.523012\pi$
$37$	−0.878750	−0.144466	−0.0722328	+	0.997388i	$0.523012\pi$
$38$	−6.16655	−1.00035
$39$	−14.5395	−2.32819
$40$	2.70604	0.427863
$41$	−5.55733	−0.867909	−0.433954	−	0.900935i	$-0.642882\pi$
$41$	−5.55733	−0.867909	−0.433954	+	0.900935i	$0.642882\pi$
$42$	−10.2261	−1.57793
$43$	3.80486	0.580236	0.290118	−	0.956991i	$-0.406305\pi$
$43$	3.80486	0.580236	0.290118	+	0.956991i	$0.406305\pi$
$44$	−3.05891	−0.461147
$45$	8.75331	1.30487
$46$	3.22341	0.475266
$47$	−11.9702	−1.74603	−0.873017	−	0.487690i	$-0.837840\pi$
$47$	−11.9702	−1.74603	−0.873017	+	0.487690i	$0.837840\pi$
$48$	2.49694	0.360403
$49$	9.77283	1.39612
$50$	2.32267	0.328475
$51$	−7.29017	−1.02083
$52$	−5.82293	−0.807495
$53$	−12.5809	−1.72813	−0.864063	−	0.503384i	$-0.832088\pi$
$53$	−12.5809	−1.72813	−0.864063	+	0.503384i	$0.832088\pi$
$54$	0.586094	0.0797574
$55$	−8.27753	−1.11614
$56$	−4.09546	−0.547279
$57$	−15.3975	−2.03945
$58$	−2.85255	−0.374558
$59$	−0.694820	−0.0904578	−0.0452289	−	0.998977i	$-0.514402\pi$
$59$	−0.694820	−0.0904578	−0.0452289	+	0.998977i	$0.514402\pi$
$60$	6.75684	0.872304
$61$	4.49934	0.576081	0.288041	−	0.957618i	$-0.406996\pi$
$61$	4.49934	0.576081	0.288041	+	0.957618i	$0.406996\pi$
$62$	1.43540	0.182295
$63$	−13.2477	−1.66905
$64$	1.00000	0.125000
$65$	−15.7571	−1.95443
$66$	−7.63791	−0.940162
$67$	6.20266	0.757776	0.378888	−	0.925443i	$-0.376307\pi$
$67$	6.20266	0.757776	0.378888	+	0.925443i	$0.376307\pi$
$68$	−2.91964	−0.354058
$69$	8.04868	0.968947
$70$	−11.0825	−1.32461
$71$	7.73550	0.918035	0.459018	−	0.888427i	$-0.348202\pi$
$71$	7.73550	0.918035	0.459018	+	0.888427i	$0.348202\pi$
$72$	3.23472	0.381216
$73$	11.7396	1.37402	0.687009	−	0.726649i	$-0.258923\pi$
$73$	11.7396	1.37402	0.687009	+	0.726649i	$0.258923\pi$
$74$	−0.878750	−0.102153
$75$	5.79958	0.669678
$76$	−6.16655	−0.707352
$77$	12.5276	1.42766
$78$	−14.5395	−1.64628
$79$	12.5656	1.41375	0.706873	−	0.707340i	$-0.250105\pi$
$79$	12.5656	1.41375	0.706873	+	0.707340i	$0.250105\pi$
$80$	2.70604	0.302545
$81$	−8.24073	−0.915637
$82$	−5.55733	−0.613704
$83$	−6.89291	−0.756595	−0.378297	−	0.925684i	$-0.623490\pi$
$83$	−6.89291	−0.756595	−0.378297	+	0.925684i	$0.623490\pi$
$84$	−10.2261	−1.11576
$85$	−7.90067	−0.856948
$86$	3.80486	0.410289
$87$	−7.12266	−0.763629
$88$	−3.05891	−0.326080
$89$	9.00125	0.954131	0.477065	−	0.878868i	$-0.341700\pi$
$89$	9.00125	0.954131	0.477065	+	0.878868i	$0.341700\pi$
$90$	8.75331	0.922680
$91$	23.8476	2.49991
$92$	3.22341	0.336064
$93$	3.58410	0.371654
$94$	−11.9702	−1.23463
$95$	−16.6870	−1.71205
$96$	2.49694	0.254843
$97$	−8.71999	−0.885381	−0.442691	−	0.896674i	$-0.645976\pi$
$97$	−8.71999	−0.885381	−0.442691	+	0.896674i	$0.645976\pi$
$98$	9.77283	0.987204
$99$	−9.89472	−0.994456
$100$	2.32267	0.232267
$101$	10.6164	1.05637	0.528186	−	0.849129i	$-0.322873\pi$
$101$	10.6164	1.05637	0.528186	+	0.849129i	$0.322873\pi$
$102$	−7.29017	−0.721834
$103$	18.6582	1.83845	0.919223	−	0.393737i	$-0.128818\pi$
$103$	18.6582	1.83845	0.919223	+	0.393737i	$0.128818\pi$
$104$	−5.82293	−0.570985
$105$	−27.6724	−2.70055
$106$	−12.5809	−1.22197
$107$	9.83282	0.950574	0.475287	−	0.879831i	$-0.342344\pi$
$107$	9.83282	0.950574	0.475287	+	0.879831i	$0.342344\pi$
$108$	0.586094	0.0563970
$109$	0.101601	0.00973160	0.00486580	−	0.999988i	$-0.498451\pi$
$109$	0.101601	0.00973160	0.00486580	+	0.999988i	$0.498451\pi$
$110$	−8.27753	−0.789232
$111$	−2.19419	−0.208263
$112$	−4.09546	−0.386985
$113$	6.52342	0.613672	0.306836	−	0.951762i	$-0.400730\pi$
$113$	6.52342	0.613672	0.306836	+	0.951762i	$0.400730\pi$
$114$	−15.3975	−1.44211
$115$	8.72269	0.813395
$116$	−2.85255	−0.264853
$117$	−18.8356	−1.74135
$118$	−0.694820	−0.0639633
$119$	11.9573	1.09612
$120$	6.75684	0.616812
$121$	−1.64310	−0.149373
$122$	4.49934	0.407351
$123$	−13.8763	−1.25119
$124$	1.43540	0.128902
$125$	−7.24497	−0.648009
$126$	−13.2477	−1.18020
$127$	−15.5749	−1.38205	−0.691024	−	0.722832i	$-0.742840\pi$
$127$	−15.5749	−1.38205	−0.691024	+	0.722832i	$0.742840\pi$
$128$	1.00000	0.0883883
$129$	9.50052	0.836474
$130$	−15.7571	−1.38199
$131$	4.28693	0.374551	0.187276	−	0.982307i	$-0.440034\pi$
$131$	4.28693	0.374551	0.187276	+	0.982307i	$0.440034\pi$
$132$	−7.63791	−0.664795
$133$	25.2549	2.18988
$134$	6.20266	0.535829
$135$	1.58600	0.136501
$136$	−2.91964	−0.250357
$137$	−9.68776	−0.827681	−0.413841	−	0.910349i	$-0.635813\pi$
$137$	−9.68776	−0.827681	−0.413841	+	0.910349i	$0.635813\pi$
$138$	8.04868	0.685149
$139$	2.91047	0.246863	0.123431	−	0.992353i	$-0.460610\pi$
$139$	2.91047	0.246863	0.123431	+	0.992353i	$0.460610\pi$
$140$	−11.0825	−0.936643
$141$	−29.8889	−2.51710
$142$	7.73550	0.649149
$143$	17.8118	1.48950
$144$	3.23472	0.269560
$145$	−7.71913	−0.641039
$146$	11.7396	0.971577
$147$	24.4022	2.01266
$148$	−0.878750	−0.0722328
$149$	−11.0892	−0.908463	−0.454231	−	0.890884i	$-0.650086\pi$
$149$	−11.0892	−0.908463	−0.454231	+	0.890884i	$0.650086\pi$
$150$	5.79958	0.473534
$151$	−7.48817	−0.609379	−0.304689	−	0.952452i	$-0.598553\pi$
$151$	−7.48817	−0.609379	−0.304689	+	0.952452i	$0.598553\pi$
$152$	−6.16655	−0.500174
$153$	−9.44423	−0.763520
$154$	12.5276	1.00951
$155$	3.88424	0.311990
$156$	−14.5395	−1.16409
$157$	3.19837	0.255258	0.127629	−	0.991822i	$-0.459263\pi$
$157$	3.19837	0.255258	0.127629	+	0.991822i	$0.459263\pi$
$158$	12.5656	0.999669
$159$	−31.4139	−2.49129
$160$	2.70604	0.213932
$161$	−13.2014	−1.04041
$162$	−8.24073	−0.647453
$163$	−12.2084	−0.956238	−0.478119	−	0.878295i	$-0.658681\pi$
$163$	−12.2084	−0.956238	−0.478119	+	0.878295i	$0.658681\pi$
$164$	−5.55733	−0.433954
$165$	−20.6685	−1.60904
$166$	−6.89291	−0.534993
$167$	−25.5277	−1.97539	−0.987695	−	0.156390i	$-0.950014\pi$
$167$	−25.5277	−1.97539	−0.987695	+	0.156390i	$0.950014\pi$
$168$	−10.2261	−0.788964
$169$	20.9065	1.60819
$170$	−7.90067	−0.605954
$171$	−19.9471	−1.52539
$172$	3.80486	0.290118
$173$	25.2263	1.91792	0.958962	−	0.283536i	$-0.0915074\pi$
$173$	25.2263	1.91792	0.958962	+	0.283536i	$0.0915074\pi$
$174$	−7.12266	−0.539967
$175$	−9.51242	−0.719071
$176$	−3.05891	−0.230574
$177$	−1.73492	−0.130405
$178$	9.00125	0.674672
$179$	16.7194	1.24967	0.624834	−	0.780758i	$-0.285167\pi$
$179$	16.7194	1.24967	0.624834	+	0.780758i	$0.285167\pi$
$180$	8.75331	0.652433
$181$	24.6080	1.82910	0.914550	−	0.404473i	$-0.132545\pi$
$181$	24.6080	1.82910	0.914550	+	0.404473i	$0.132545\pi$
$182$	23.8476	1.76770
$183$	11.2346	0.830485
$184$	3.22341	0.237633
$185$	−2.37794	−0.174829
$186$	3.58410	0.262799
$187$	8.93090	0.653092
$188$	−11.9702	−0.873017
$189$	−2.40033	−0.174598
$190$	−16.6870	−1.21060
$191$	−15.2975	−1.10689	−0.553446	−	0.832885i	$-0.686687\pi$
$191$	−15.2975	−1.10689	−0.553446	+	0.832885i	$0.686687\pi$
$192$	2.49694	0.180201
$193$	−20.0164	−1.44081	−0.720406	−	0.693553i	$-0.756044\pi$
$193$	−20.0164	−1.44081	−0.720406	+	0.693553i	$0.756044\pi$
$194$	−8.71999	−0.626059
$195$	−39.3446	−2.81752
$196$	9.77283	0.698059
$197$	0.744839	0.0530676	0.0265338	−	0.999648i	$-0.491553\pi$
$197$	0.744839	0.0530676	0.0265338	+	0.999648i	$0.491553\pi$
$198$	−9.89472	−0.703187
$199$	−16.8372	−1.19356	−0.596779	−	0.802405i	$-0.703553\pi$
$199$	−16.8372	−1.19356	−0.596779	+	0.802405i	$0.703553\pi$
$200$	2.32267	0.164238
$201$	15.4877	1.09242
$202$	10.6164	0.746967
$203$	11.6825	0.819952
$204$	−7.29017	−0.510414
$205$	−15.0384	−1.05033
$206$	18.6582	1.29998
$207$	10.4269	0.724716
$208$	−5.82293	−0.403748
$209$	18.8629	1.30477
$210$	−27.6724	−1.90958
$211$	19.8775	1.36842	0.684212	−	0.729283i	$-0.260146\pi$
$211$	19.8775	1.36842	0.684212	+	0.729283i	$0.260146\pi$
$212$	−12.5809	−0.864063
$213$	19.3151	1.32345
$214$	9.83282	0.672158
$215$	10.2961	0.702190
$216$	0.586094	0.0398787
$217$	−5.87861	−0.399066
$218$	0.101601	0.00688128
$219$	29.3132	1.98080
$220$	−8.27753	−0.558071
$221$	17.0008	1.14360
$222$	−2.19419	−0.147264
$223$	0.398635	0.0266946	0.0133473	−	0.999911i	$-0.495751\pi$
$223$	0.398635	0.0266946	0.0133473	+	0.999911i	$0.495751\pi$
$224$	−4.09546	−0.273640
$225$	7.51321	0.500880
$226$	6.52342	0.433931
$227$	−10.4383	−0.692811	−0.346406	−	0.938085i	$-0.612598\pi$
$227$	−10.4383	−0.692811	−0.346406	+	0.938085i	$0.612598\pi$
$228$	−15.3975	−1.01973
$229$	4.96378	0.328016	0.164008	−	0.986459i	$-0.447558\pi$
$229$	4.96378	0.328016	0.164008	+	0.986459i	$0.447558\pi$
$230$	8.72269	0.575157
$231$	31.2808	2.05813
$232$	−2.85255	−0.187279
$233$	−23.1950	−1.51956	−0.759778	−	0.650182i	$-0.774693\pi$
$233$	−23.1950	−1.51956	−0.759778	+	0.650182i	$0.774693\pi$
$234$	−18.8356	−1.23132
$235$	−32.3919	−2.11301
$236$	−0.694820	−0.0452289
$237$	31.3757	2.03807
$238$	11.9573	0.775075
$239$	6.72223	0.434825	0.217412	−	0.976080i	$-0.430238\pi$
$239$	6.72223	0.434825	0.217412	+	0.976080i	$0.430238\pi$
$240$	6.75684	0.436152
$241$	−0.430993	−0.0277627	−0.0138813	−	0.999904i	$-0.504419\pi$
$241$	−0.430993	−0.0277627	−0.0138813	+	0.999904i	$0.504419\pi$
$242$	−1.64310	−0.105622
$243$	−22.3349	−1.43279
$244$	4.49934	0.288041
$245$	26.4457	1.68955
$246$	−13.8763	−0.884723
$247$	35.9074	2.28473
$248$	1.43540	0.0911477
$249$	−17.2112	−1.09072
$250$	−7.24497	−0.458212
$251$	12.5032	0.789196	0.394598	−	0.918854i	$-0.370884\pi$
$251$	12.5032	0.789196	0.394598	+	0.918854i	$0.370884\pi$
$252$	−13.2477	−0.834527
$253$	−9.86011	−0.619900
$254$	−15.5749	−0.977255
$255$	−19.7275	−1.23539
$256$	1.00000	0.0625000
$257$	−0.268758	−0.0167646	−0.00838232	−	0.999965i	$-0.502668\pi$
$257$	−0.268758	−0.0167646	−0.00838232	+	0.999965i	$0.502668\pi$
$258$	9.50052	0.591477
$259$	3.59889	0.223624
$260$	−15.7571	−0.977214
$261$	−9.22722	−0.571150
$262$	4.28693	0.264848
$263$	−15.6621	−0.965766	−0.482883	−	0.875685i	$-0.660410\pi$
$263$	−15.6621	−0.965766	−0.482883	+	0.875685i	$0.660410\pi$
$264$	−7.63791	−0.470081
$265$	−34.0446	−2.09134
$266$	25.2549	1.54848
$267$	22.4756	1.37549
$268$	6.20266	0.378888
$269$	−6.49759	−0.396165	−0.198082	−	0.980185i	$-0.563471\pi$
$269$	−6.49759	−0.396165	−0.198082	+	0.980185i	$0.563471\pi$
$270$	1.58600	0.0965207
$271$	11.0077	0.668670	0.334335	−	0.942454i	$-0.391488\pi$
$271$	11.0077	0.668670	0.334335	+	0.942454i	$0.391488\pi$
$272$	−2.91964	−0.177029
$273$	59.5461	3.60389
$274$	−9.68776	−0.585259
$275$	−7.10483	−0.428438
$276$	8.04868	0.484473
$277$	−6.56787	−0.394625	−0.197313	−	0.980341i	$-0.563221\pi$
$277$	−6.56787	−0.394625	−0.197313	+	0.980341i	$0.563221\pi$
$278$	2.91047	0.174558
$279$	4.64311	0.277976
$280$	−11.0825	−0.662306
$281$	14.0873	0.840379	0.420190	−	0.907436i	$-0.361964\pi$
$281$	14.0873	0.840379	0.420190	+	0.907436i	$0.361964\pi$
$282$	−29.8889	−1.77986
$283$	−30.7015	−1.82501	−0.912507	−	0.409060i	$-0.865857\pi$
$283$	−30.7015	−1.82501	−0.912507	+	0.409060i	$0.865857\pi$
$284$	7.73550	0.459018
$285$	−41.6664	−2.46810
$286$	17.8118	1.05323
$287$	22.7598	1.34347
$288$	3.23472	0.190608
$289$	−8.47571	−0.498571
$290$	−7.71913	−0.453283
$291$	−21.7733	−1.27637
$292$	11.7396	0.687009
$293$	−24.0835	−1.40697	−0.703486	−	0.710709i	$-0.748374\pi$
$293$	−24.0835	−1.40697	−0.703486	+	0.710709i	$0.748374\pi$
$294$	24.4022	1.42316
$295$	−1.88021	−0.109470
$296$	−0.878750	−0.0510763
$297$	−1.79281	−0.104029
$298$	−11.0892	−0.642380
$299$	−18.7697	−1.08548
$300$	5.79958	0.334839
$301$	−15.5827	−0.898170
$302$	−7.48817	−0.430896
$303$	26.5085	1.52288
$304$	−6.16655	−0.353676
$305$	12.1754	0.697161
$306$	−9.44423	−0.539890
$307$	−13.6747	−0.780457	−0.390228	−	0.920718i	$-0.627604\pi$
$307$	−13.6747	−0.780457	−0.390228	+	0.920718i	$0.627604\pi$
$308$	12.5276	0.713828
$309$	46.5885	2.65032
$310$	3.88424	0.220610
$311$	28.8618	1.63660	0.818302	−	0.574788i	$-0.194916\pi$
$311$	28.8618	1.63660	0.818302	+	0.574788i	$0.194916\pi$
$312$	−14.5395	−0.823138
$313$	5.62377	0.317874	0.158937	−	0.987289i	$-0.449193\pi$
$313$	5.62377	0.317874	0.158937	+	0.987289i	$0.449193\pi$
$314$	3.19837	0.180495
$315$	−35.8489	−2.01985
$316$	12.5656	0.706873
$317$	31.3447	1.76049	0.880247	−	0.474515i	$-0.157377\pi$
$317$	31.3447	1.76049	0.880247	+	0.474515i	$0.157377\pi$
$318$	−31.4139	−1.76160
$319$	8.72568	0.488544
$320$	2.70604	0.151272
$321$	24.5520	1.37036
$322$	−13.2014	−0.735683
$323$	18.0041	1.00178
$324$	−8.24073	−0.457818
$325$	−13.5248	−0.750219
$326$	−12.2084	−0.676163
$327$	0.253692	0.0140292
$328$	−5.55733	−0.306852
$329$	49.0236	2.70276
$330$	−20.6685	−1.13776
$331$	−13.9136	−0.764762	−0.382381	−	0.924005i	$-0.624896\pi$
$331$	−13.9136	−0.764762	−0.382381	+	0.924005i	$0.624896\pi$
$332$	−6.89291	−0.378297
$333$	−2.84252	−0.155769
$334$	−25.5277	−1.39681
$335$	16.7847	0.917045
$336$	−10.2261	−0.557882
$337$	−28.3455	−1.54408	−0.772040	−	0.635574i	$-0.780763\pi$
$337$	−28.3455	−1.54408	−0.772040	+	0.635574i	$0.780763\pi$
$338$	20.9065	1.13716
$339$	16.2886	0.884676
$340$	−7.90067	−0.428474
$341$	−4.39074	−0.237772
$342$	−19.9471	−1.07862
$343$	−11.3560	−0.613167
$344$	3.80486	0.205144
$345$	21.7801	1.17260
$346$	25.2263	1.35618
$347$	−27.0776	−1.45360	−0.726801	−	0.686848i	$-0.758994\pi$
$347$	−27.0776	−1.45360	−0.726801	+	0.686848i	$0.758994\pi$
$348$	−7.12266	−0.381815
$349$	−5.37555	−0.287747	−0.143873	−	0.989596i	$-0.545956\pi$
$349$	−5.37555	−0.287747	−0.143873	+	0.989596i	$0.545956\pi$
$350$	−9.51242	−0.508460
$351$	−3.41279	−0.182161
$352$	−3.05891	−0.163040
$353$	−8.72558	−0.464416	−0.232208	−	0.972666i	$-0.574595\pi$
$353$	−8.72558	−0.464416	−0.232208	+	0.972666i	$0.574595\pi$
$354$	−1.73492	−0.0922102
$355$	20.9326	1.11099
$356$	9.00125	0.477065
$357$	29.8566	1.58018
$358$	16.7194	0.883648
$359$	27.1804	1.43452	0.717262	−	0.696803i	$-0.245395\pi$
$359$	27.1804	1.43452	0.717262	+	0.696803i	$0.245395\pi$
$360$	8.75331	0.461340
$361$	19.0264	1.00139
$362$	24.6080	1.29337
$363$	−4.10272	−0.215337
$364$	23.8476	1.24995
$365$	31.7679	1.66281
$366$	11.2346	0.587241
$367$	−28.7648	−1.50151	−0.750755	−	0.660581i	$-0.770310\pi$
$367$	−28.7648	−1.50151	−0.750755	+	0.660581i	$0.770310\pi$
$368$	3.22341	0.168032
$369$	−17.9764	−0.935815
$370$	−2.37794	−0.123623
$371$	51.5248	2.67504
$372$	3.58410	0.185827
$373$	11.8068	0.611333	0.305667	−	0.952139i	$-0.401121\pi$
$373$	11.8068	0.611333	0.305667	+	0.952139i	$0.401121\pi$
$374$	8.93090	0.461806
$375$	−18.0903	−0.934177
$376$	−11.9702	−0.617316
$377$	16.6102	0.855469
$378$	−2.40033	−0.123460
$379$	−7.98352	−0.410086	−0.205043	−	0.978753i	$-0.565733\pi$
$379$	−7.98352	−0.410086	−0.205043	+	0.978753i	$0.565733\pi$
$380$	−16.6870	−0.856023
$381$	−38.8896	−1.99237
$382$	−15.2975	−0.782690
$383$	−33.9167	−1.73306	−0.866532	−	0.499121i	$-0.833656\pi$
$383$	−33.9167	−1.73306	−0.866532	+	0.499121i	$0.833656\pi$
$384$	2.49694	0.127422
$385$	33.9003	1.72772
$386$	−20.0164	−1.01881
$387$	12.3077	0.625634
$388$	−8.71999	−0.442691
$389$	−5.23742	−0.265548	−0.132774	−	0.991146i	$-0.542388\pi$
$389$	−5.23742	−0.265548	−0.132774	+	0.991146i	$0.542388\pi$
$390$	−39.3446	−1.99229
$391$	−9.41120	−0.475945
$392$	9.77283	0.493602
$393$	10.7042	0.539957
$394$	0.744839	0.0375244
$395$	34.0032	1.71089
$396$	−9.89472	−0.497228
$397$	−6.77144	−0.339849	−0.169924	−	0.985457i	$-0.554352\pi$
$397$	−6.77144	−0.339849	−0.169924	+	0.985457i	$0.554352\pi$
$398$	−16.8372	−0.843973
$399$	63.0601	3.15695
$400$	2.32267	0.116134
$401$	−25.6042	−1.27861	−0.639306	−	0.768952i	$-0.720778\pi$
$401$	−25.6042	−1.27861	−0.639306	+	0.768952i	$0.720778\pi$
$402$	15.4877	0.772456
$403$	−8.35821	−0.416352
$404$	10.6164	0.528186
$405$	−22.2998	−1.10808
$406$	11.6825	0.579794
$407$	2.68801	0.133240
$408$	−7.29017	−0.360917
$409$	−17.5388	−0.867238	−0.433619	−	0.901096i	$-0.642764\pi$
$409$	−17.5388	−0.867238	−0.433619	+	0.901096i	$0.642764\pi$
$410$	−15.0384	−0.742692
$411$	−24.1898	−1.19319
$412$	18.6582	0.919223
$413$	2.84561	0.140023
$414$	10.4269	0.512452
$415$	−18.6525	−0.915616
$416$	−5.82293	−0.285493
$417$	7.26728	0.355880
$418$	18.8629	0.922615
$419$	−1.22367	−0.0597799	−0.0298900	−	0.999553i	$-0.509516\pi$
$419$	−1.22367	−0.0597799	−0.0298900	+	0.999553i	$0.509516\pi$
$420$	−27.6724	−1.35027
$421$	−24.8823	−1.21269	−0.606344	−	0.795202i	$-0.707365\pi$
$421$	−24.8823	−1.21269	−0.606344	+	0.795202i	$0.707365\pi$
$422$	19.8775	0.967622
$423$	−38.7203	−1.88265
$424$	−12.5809	−0.610985
$425$	−6.78136	−0.328944
$426$	19.3151	0.935820
$427$	−18.4269	−0.891739
$428$	9.83282	0.475287
$429$	44.4750	2.14727
$430$	10.2961	0.496523
$431$	11.2312	0.540987	0.270494	−	0.962722i	$-0.412813\pi$
$431$	11.2312	0.540987	0.270494	+	0.962722i	$0.412813\pi$
$432$	0.586094	0.0281985
$433$	16.6998	0.802539	0.401270	−	0.915960i	$-0.368569\pi$
$433$	16.6998	0.802539	0.401270	+	0.915960i	$0.368569\pi$
$434$	−5.87861	−0.282182
$435$	−19.2742	−0.924128
$436$	0.101601	0.00486580
$437$	−19.8773	−0.950862
$438$	29.3132	1.40064
$439$	−13.9250	−0.664603	−0.332302	−	0.943173i	$-0.607825\pi$
$439$	−13.9250	−0.664603	−0.332302	+	0.943173i	$0.607825\pi$
$440$	−8.27753	−0.394616
$441$	31.6124	1.50535
$442$	17.0008	0.808648
$443$	18.8161	0.893979	0.446990	−	0.894539i	$-0.352496\pi$
$443$	18.8161	0.893979	0.446990	+	0.894539i	$0.352496\pi$
$444$	−2.19419	−0.104132
$445$	24.3578	1.15467
$446$	0.398635	0.0188759
$447$	−27.6891	−1.30965
$448$	−4.09546	−0.193492
$449$	−14.2232	−0.671235	−0.335618	−	0.941998i	$-0.608945\pi$
$449$	−14.2232	−0.671235	−0.335618	+	0.941998i	$0.608945\pi$
$450$	7.51321	0.354176
$451$	16.9993	0.800468
$452$	6.52342	0.306836
$453$	−18.6975	−0.878487
$454$	−10.4383	−0.489892
$455$	64.5326	3.02534
$456$	−15.3975	−0.721056
$457$	−20.4935	−0.958644	−0.479322	−	0.877639i	$-0.659117\pi$
$457$	−20.4935	−0.958644	−0.479322	+	0.877639i	$0.659117\pi$
$458$	4.96378	0.231942
$459$	−1.71118	−0.0798712
$460$	8.72269	0.406698
$461$	−39.6905	−1.84857	−0.924286	−	0.381702i	$-0.875338\pi$
$461$	−39.6905	−1.84857	−0.924286	+	0.381702i	$0.875338\pi$
$462$	31.2808	1.45531
$463$	16.6062	0.771754	0.385877	−	0.922550i	$-0.373899\pi$
$463$	16.6062	0.771754	0.385877	+	0.922550i	$0.373899\pi$
$464$	−2.85255	−0.132426
$465$	9.69874	0.449768
$466$	−23.1950	−1.07449
$467$	27.3935	1.26762	0.633809	−	0.773490i	$-0.281490\pi$
$467$	27.3935	1.26762	0.633809	+	0.773490i	$0.281490\pi$
$468$	−18.8356	−0.870675
$469$	−25.4028	−1.17299
$470$	−32.3919	−1.49413
$471$	7.98616	0.367983
$472$	−0.694820	−0.0319817
$473$	−11.6387	−0.535148
$474$	31.3757	1.44113
$475$	−14.3229	−0.657179
$476$	11.9573	0.548061
$477$	−40.6959	−1.86334
$478$	6.72223	0.307468
$479$	−1.87016	−0.0854499	−0.0427250	−	0.999087i	$-0.513604\pi$
$479$	−1.87016	−0.0854499	−0.0427250	+	0.999087i	$0.513604\pi$
$480$	6.75684	0.308406
$481$	5.11690	0.233311
$482$	−0.430993	−0.0196312
$483$	−32.9631	−1.49987
$484$	−1.64310	−0.0746863
$485$	−23.5967	−1.07147
$486$	−22.3349	−1.01313
$487$	42.9867	1.94791	0.973957	−	0.226731i	$-0.0728038\pi$
$487$	42.9867	1.94791	0.973957	+	0.226731i	$0.0728038\pi$
$488$	4.49934	0.203675
$489$	−30.4838	−1.37852
$490$	26.4457	1.19469
$491$	1.83166	0.0826619	0.0413309	−	0.999146i	$-0.486840\pi$
$491$	1.83166	0.0826619	0.0413309	+	0.999146i	$0.486840\pi$
$492$	−13.8763	−0.625593
$493$	8.32842	0.375093
$494$	35.9074	1.61555
$495$	−26.7755	−1.20347
$496$	1.43540	0.0644512
$497$	−31.6805	−1.42106
$498$	−17.2112	−0.771252
$499$	−3.05287	−0.136665	−0.0683325	−	0.997663i	$-0.521768\pi$
$499$	−3.05287	−0.136665	−0.0683325	+	0.997663i	$0.521768\pi$
$500$	−7.24497	−0.324005
$501$	−63.7411	−2.84774
$502$	12.5032	0.558046
$503$	8.65544	0.385927	0.192964	−	0.981206i	$-0.438190\pi$
$503$	8.65544	0.385927	0.192964	+	0.981206i	$0.438190\pi$
$504$	−13.2477	−0.590099
$505$	28.7284	1.27840
$506$	−9.86011	−0.438335
$507$	52.2024	2.31839
$508$	−15.5749	−0.691024
$509$	−22.2366	−0.985621	−0.492811	−	0.870137i	$-0.664030\pi$
$509$	−22.2366	−0.985621	−0.492811	+	0.870137i	$0.664030\pi$
$510$	−19.7275	−0.873549
$511$	−48.0792	−2.12690
$512$	1.00000	0.0441942
$513$	−3.61418	−0.159570
$514$	−0.268758	−0.0118544
$515$	50.4899	2.22485
$516$	9.50052	0.418237
$517$	36.6157	1.61036
$518$	3.59889	0.158126
$519$	62.9887	2.76490
$520$	−15.7571	−0.690995
$521$	18.9352	0.829567	0.414783	−	0.909920i	$-0.363857\pi$
$521$	18.9352	0.829567	0.414783	+	0.909920i	$0.363857\pi$
$522$	−9.22722	−0.403864
$523$	27.9007	1.22001	0.610006	−	0.792397i	$-0.291167\pi$
$523$	27.9007	1.22001	0.610006	+	0.792397i	$0.291167\pi$
$524$	4.28693	0.187276
$525$	−23.7520	−1.03662
$526$	−15.6621	−0.682900
$527$	−4.19084	−0.182556
$528$	−7.63791	−0.332397
$529$	−12.6096	−0.548244
$530$	−34.0446	−1.47880
$531$	−2.24755	−0.0975354
$532$	25.2549	1.09494
$533$	32.3599	1.40166
$534$	22.4756	0.972615
$535$	26.6080	1.15037
$536$	6.20266	0.267914
$537$	41.7474	1.80153
$538$	−6.49759	−0.280131
$539$	−29.8941	−1.28763
$540$	1.58600	0.0682505
$541$	−30.2839	−1.30201	−0.651003	−	0.759075i	$-0.725652\pi$
$541$	−30.2839	−1.30201	−0.651003	+	0.759075i	$0.725652\pi$
$542$	11.0077	0.472821
$543$	61.4448	2.63685
$544$	−2.91964	−0.125178
$545$	0.274937	0.0117770
$546$	59.5461	2.54834
$547$	5.81677	0.248707	0.124353	−	0.992238i	$-0.460314\pi$
$547$	5.81677	0.248707	0.124353	+	0.992238i	$0.460314\pi$
$548$	−9.68776	−0.413841
$549$	14.5541	0.621155
$550$	−7.10483	−0.302951
$551$	17.5904	0.749377
$552$	8.04868	0.342574
$553$	−51.4622	−2.18839
$554$	−6.56787	−0.279042
$555$	−5.93757	−0.252036
$556$	2.91047	0.123431
$557$	−21.6060	−0.915477	−0.457738	−	0.889087i	$-0.651340\pi$
$557$	−21.6060	−0.915477	−0.457738	+	0.889087i	$0.651340\pi$
$558$	4.64311	0.196559
$559$	−22.1554	−0.937075
$560$	−11.0825	−0.468321
$561$	22.2999	0.941504
$562$	14.0873	0.594238
$563$	30.5259	1.28651	0.643257	−	0.765650i	$-0.277583\pi$
$563$	30.5259	1.28651	0.643257	+	0.765650i	$0.277583\pi$
$564$	−29.8889	−1.25855
$565$	17.6527	0.742653
$566$	−30.7015	−1.29048
$567$	33.7496	1.41735
$568$	7.73550	0.324574
$569$	−19.7501	−0.827966	−0.413983	−	0.910285i	$-0.635863\pi$
$569$	−19.7501	−0.827966	−0.413983	+	0.910285i	$0.635863\pi$
$570$	−41.6664	−1.74521
$571$	−22.0718	−0.923674	−0.461837	−	0.886965i	$-0.652810\pi$
$571$	−22.0718	−0.923674	−0.461837	+	0.886965i	$0.652810\pi$
$572$	17.8118	0.744748
$573$	−38.1971	−1.59571
$574$	22.7598	0.949977
$575$	7.48693	0.312227
$576$	3.23472	0.134780
$577$	8.18291	0.340659	0.170329	−	0.985387i	$-0.445517\pi$
$577$	8.18291	0.340659	0.170329	+	0.985387i	$0.445517\pi$
$578$	−8.47571	−0.352543
$579$	−49.9798	−2.07709
$580$	−7.71913	−0.320519
$581$	28.2297	1.17116
$582$	−21.7733	−0.902533
$583$	38.4839	1.59384
$584$	11.7396	0.485789
$585$	−50.9699	−2.10735
$586$	−24.0835	−0.994879
$587$	−16.1291	−0.665721	−0.332861	−	0.942976i	$-0.608014\pi$
$587$	−16.1291	−0.665721	−0.332861	+	0.942976i	$0.608014\pi$
$588$	24.4022	1.00633
$589$	−8.85145	−0.364718
$590$	−1.88021	−0.0774071
$591$	1.85982	0.0765028
$592$	−0.878750	−0.0361164
$593$	42.2771	1.73611	0.868057	−	0.496465i	$-0.165369\pi$
$593$	42.2771	1.73611	0.868057	+	0.496465i	$0.165369\pi$
$594$	−1.79281	−0.0735598
$595$	32.3569	1.32650
$596$	−11.0892	−0.454231
$597$	−42.0416	−1.72065
$598$	−18.7697	−0.767550
$599$	−34.2597	−1.39981	−0.699906	−	0.714235i	$-0.746775\pi$
$599$	−34.2597	−1.39981	−0.699906	+	0.714235i	$0.746775\pi$
$600$	5.79958	0.236767
$601$	−42.9599	−1.75237	−0.876186	−	0.481972i	$-0.839921\pi$
$601$	−42.9599	−1.75237	−0.876186	+	0.481972i	$0.839921\pi$
$602$	−15.5827	−0.635102
$603$	20.0639	0.817066
$604$	−7.48817	−0.304689
$605$	−4.44630	−0.180768
$606$	26.5085	1.07684
$607$	20.2262	0.820955	0.410478	−	0.911871i	$-0.365362\pi$
$607$	20.2262	0.820955	0.410478	+	0.911871i	$0.365362\pi$
$608$	−6.16655	−0.250087
$609$	29.1706	1.18205
$610$	12.1754	0.492968
$611$	69.7017	2.81983
$612$	−9.44423	−0.381760
$613$	6.46985	0.261315	0.130657	−	0.991428i	$-0.458291\pi$
$613$	6.46985	0.261315	0.130657	+	0.991428i	$0.458291\pi$
$614$	−13.6747	−0.551866
$615$	−37.5500	−1.51416
$616$	12.5276	0.504753
$617$	0.0126515	0.000509331 0	0.000254665	−	1.00000i	$-0.499919\pi$
$617$	0.0126515	0.000509331 0	0.000254665		1.00000i	$0.499919\pi$
$618$	46.5885	1.87406
$619$	−30.8857	−1.24140	−0.620701	−	0.784047i	$-0.713152\pi$
$619$	−30.8857	−1.24140	−0.620701	+	0.784047i	$0.713152\pi$
$620$	3.88424	0.155995
$621$	1.88922	0.0758119
$622$	28.8618	1.15725
$623$	−36.8643	−1.47694
$624$	−14.5395	−0.582047
$625$	−31.2186	−1.24874
$626$	5.62377	0.224771
$627$	47.0996	1.88098
$628$	3.19837	0.127629
$629$	2.56563	0.102299
$630$	−35.8489	−1.42825
$631$	43.2593	1.72212	0.861062	−	0.508499i	$-0.169800\pi$
$631$	43.2593	1.72212	0.861062	+	0.508499i	$0.169800\pi$
$632$	12.5656	0.499835
$633$	49.6330	1.97274
$634$	31.3447	1.24486
$635$	−42.1463	−1.67253
$636$	−31.4139	−1.24564
$637$	−56.9065	−2.25472
$638$	8.72568	0.345453
$639$	25.0222	0.989864
$640$	2.70604	0.106966
$641$	38.5070	1.52093	0.760467	−	0.649377i	$-0.224970\pi$
$641$	38.5070	1.52093	0.760467	+	0.649377i	$0.224970\pi$
$642$	24.5520	0.968990
$643$	−3.36617	−0.132749	−0.0663745	−	0.997795i	$-0.521143\pi$
$643$	−3.36617	−0.132749	−0.0663745	+	0.997795i	$0.521143\pi$
$644$	−13.2014	−0.520207
$645$	25.7088	1.01228
$646$	18.0041	0.708362
$647$	13.2836	0.522234	0.261117	−	0.965307i	$-0.415909\pi$
$647$	13.2836	0.522234	0.261117	+	0.965307i	$0.415909\pi$
$648$	−8.24073	−0.323726
$649$	2.12539	0.0834287
$650$	−13.5248	−0.530485
$651$	−14.6786	−0.575298
$652$	−12.2084	−0.478119
$653$	4.53778	0.177577	0.0887886	−	0.996050i	$-0.471700\pi$
$653$	4.53778	0.177577	0.0887886	+	0.996050i	$0.471700\pi$
$654$	0.253692	0.00992013
$655$	11.6006	0.453274
$656$	−5.55733	−0.216977
$657$	37.9744	1.48152
$658$	49.0236	1.91114
$659$	−16.9944	−0.662008	−0.331004	−	0.943629i	$-0.607387\pi$
$659$	−16.9944	−0.662008	−0.331004	+	0.943629i	$0.607387\pi$
$660$	−20.6685	−0.804521
$661$	11.9617	0.465258	0.232629	−	0.972566i	$-0.425267\pi$
$661$	11.9617	0.465258	0.232629	+	0.972566i	$0.425267\pi$
$662$	−13.9136	−0.540768
$663$	42.4502	1.64863
$664$	−6.89291	−0.267497
$665$	68.3409	2.65015
$666$	−2.84252	−0.110145
$667$	−9.19495	−0.356030
$668$	−25.5277	−0.987695
$669$	0.995369	0.0384832
$670$	16.7847	0.648449
$671$	−13.7630	−0.531316
$672$	−10.2261	−0.394482
$673$	28.1973	1.08693	0.543464	−	0.839433i	$-0.317113\pi$
$673$	28.1973	1.08693	0.543464	+	0.839433i	$0.317113\pi$
$674$	−28.3455	−1.09183
$675$	1.36131	0.0523967
$676$	20.9065	0.804096
$677$	−31.3267	−1.20398	−0.601991	−	0.798503i	$-0.705626\pi$
$677$	−31.3267	−1.20398	−0.601991	+	0.798503i	$0.705626\pi$
$678$	16.2886	0.625560
$679$	35.7124	1.37052
$680$	−7.90067	−0.302977
$681$	−26.0637	−0.998764
$682$	−4.39074	−0.168130
$683$	30.4860	1.16651	0.583257	−	0.812287i	$-0.301778\pi$
$683$	30.4860	1.16651	0.583257	+	0.812287i	$0.301778\pi$
$684$	−19.9471	−0.762697
$685$	−26.2155	−1.00164
$686$	−11.3560	−0.433574
$687$	12.3943	0.472871
$688$	3.80486	0.145059
$689$	73.2580	2.79091
$690$	21.7801	0.829153
$691$	−3.77582	−0.143639	−0.0718195	−	0.997418i	$-0.522881\pi$
$691$	−3.77582	−0.143639	−0.0718195	+	0.997418i	$0.522881\pi$
$692$	25.2263	0.958962
$693$	40.5235	1.53936
$694$	−27.0776	−1.02785
$695$	7.87586	0.298748
$696$	−7.12266	−0.269984
$697$	16.2254	0.614580
$698$	−5.37555	−0.203468
$699$	−57.9167	−2.19061
$700$	−9.51242	−0.359536
$701$	29.0353	1.09665	0.548324	−	0.836266i	$-0.315266\pi$
$701$	29.0353	1.09665	0.548324	+	0.836266i	$0.315266\pi$
$702$	−3.41279	−0.128807
$703$	5.41886	0.204376
$704$	−3.05891	−0.115287
$705$	−80.8807	−3.04615
$706$	−8.72558	−0.328392
$707$	−43.4791	−1.63520
$708$	−1.73492	−0.0652025
$709$	16.3429	0.613771	0.306886	−	0.951746i	$-0.400713\pi$
$709$	16.3429	0.613771	0.306886	+	0.951746i	$0.400713\pi$
$710$	20.9326	0.785587
$711$	40.6464	1.52436
$712$	9.00125	0.337336
$713$	4.62687	0.173278
$714$	29.8566	1.11736
$715$	48.1995	1.80256
$716$	16.7194	0.624834
$717$	16.7850	0.626848
$718$	27.1804	1.01436
$719$	4.52128	0.168615	0.0843077	−	0.996440i	$-0.473132\pi$
$719$	4.52128	0.168615	0.0843077	+	0.996440i	$0.473132\pi$
$720$	8.75331	0.326216
$721$	−76.4140	−2.84580
$722$	19.0264	0.708089
$723$	−1.07616	−0.0400230
$724$	24.6080	0.914550
$725$	−6.62554	−0.246066
$726$	−4.10272	−0.152266
$727$	−42.2429	−1.56670	−0.783351	−	0.621580i	$-0.786491\pi$
$727$	−42.2429	−1.56670	−0.783351	+	0.621580i	$0.786491\pi$
$728$	23.8476	0.883851
$729$	−31.0468	−1.14988
$730$	31.7679	1.17578
$731$	−11.1088	−0.410874
$732$	11.2346	0.415242
$733$	−19.2718	−0.711818	−0.355909	−	0.934521i	$-0.615829\pi$
$733$	−19.2718	−0.711818	−0.355909	+	0.934521i	$0.615829\pi$
$734$	−28.7648	−1.06173
$735$	66.0334	2.43568
$736$	3.22341	0.118817
$737$	−18.9734	−0.698893
$738$	−17.9764	−0.661721
$739$	36.1088	1.32828	0.664142	−	0.747606i	$-0.268797\pi$
$739$	36.1088	1.32828	0.664142	+	0.747606i	$0.268797\pi$
$740$	−2.37794	−0.0874147
$741$	89.6588	3.29370
$742$	51.5248	1.89154
$743$	−5.91985	−0.217178	−0.108589	−	0.994087i	$-0.534633\pi$
$743$	−5.91985	−0.217178	−0.108589	+	0.994087i	$0.534633\pi$
$744$	3.58410	0.131400
$745$	−30.0079	−1.09940
$746$	11.8068	0.432278
$747$	−22.2967	−0.815792
$748$	8.93090	0.326546
$749$	−40.2699	−1.47143
$750$	−18.0903	−0.660563
$751$	42.2909	1.54322	0.771609	−	0.636097i	$-0.219452\pi$
$751$	42.2909	1.54322	0.771609	+	0.636097i	$0.219452\pi$
$752$	−11.9702	−0.436509
$753$	31.2198	1.13771
$754$	16.6102	0.604908
$755$	−20.2633	−0.737458
$756$	−2.40033	−0.0872991
$757$	−14.6489	−0.532424	−0.266212	−	0.963914i	$-0.585772\pi$
$757$	−14.6489	−0.532424	−0.266212	+	0.963914i	$0.585772\pi$
$758$	−7.98352	−0.289974
$759$	−24.6201	−0.893654
$760$	−16.6870	−0.605300
$761$	−43.0858	−1.56186	−0.780930	−	0.624618i	$-0.785255\pi$
$761$	−43.0858	−1.56186	−0.780930	+	0.624618i	$0.785255\pi$
$762$	−38.8896	−1.40882
$763$	−0.416103	−0.0150639
$764$	−15.2975	−0.553446
$765$	−25.5565	−0.923997
$766$	−33.9167	−1.22546
$767$	4.04589	0.146088
$768$	2.49694	0.0901007
$769$	−10.4029	−0.375138	−0.187569	−	0.982251i	$-0.560061\pi$
$769$	−10.4029	−0.375138	−0.187569	+	0.982251i	$0.560061\pi$
$770$	33.9003	1.22168
$771$	−0.671073	−0.0241681
$772$	−20.0164	−0.720406
$773$	−29.3686	−1.05631	−0.528157	−	0.849147i	$-0.677117\pi$
$773$	−29.3686	−1.05631	−0.528157	+	0.849147i	$0.677117\pi$
$774$	12.3077	0.442390
$775$	3.33395	0.119759
$776$	−8.71999	−0.313029
$777$	8.98623	0.322379
$778$	−5.23742	−0.187771
$779$	34.2696	1.22783
$780$	−39.3446	−1.40876
$781$	−23.6622	−0.846699
$782$	−9.41120	−0.336544
$783$	−1.67186	−0.0597476
$784$	9.77283	0.349029
$785$	8.65494	0.308908
$786$	10.7042	0.381807
$787$	42.8657	1.52800	0.763998	−	0.645218i	$-0.223234\pi$
$787$	42.8657	1.52800	0.763998	+	0.645218i	$0.223234\pi$
$788$	0.744839	0.0265338
$789$	−39.1074	−1.39226
$790$	34.0032	1.20978
$791$	−26.7164	−0.949927
$792$	−9.89472	−0.351593
$793$	−26.1993	−0.930365
$794$	−6.77144	−0.240309
$795$	−85.0074	−3.01490
$796$	−16.8372	−0.596779
$797$	−21.1675	−0.749791	−0.374895	−	0.927067i	$-0.622321\pi$
$797$	−21.1675	−0.749791	−0.374895	+	0.927067i	$0.622321\pi$
$798$	63.0601	2.23230
$799$	34.9487	1.23640
$800$	2.32267	0.0821189
$801$	29.1166	1.02878
$802$	−25.6042	−0.904116
$803$	−35.9104	−1.26725
$804$	15.4877	0.546209
$805$	−35.7235	−1.25909
$806$	−8.35821	−0.294405
$807$	−16.2241	−0.571116
$808$	10.6164	0.373484
$809$	−5.34944	−0.188076	−0.0940381	−	0.995569i	$-0.529978\pi$
$809$	−5.34944	−0.188076	−0.0940381	+	0.995569i	$0.529978\pi$
$810$	−22.2998	−0.783534
$811$	−1.51689	−0.0532651	−0.0266325	−	0.999645i	$-0.508478\pi$
$811$	−1.51689	−0.0532651	−0.0266325	+	0.999645i	$0.508478\pi$
$812$	11.6825	0.409976
$813$	27.4856	0.963962
$814$	2.68801	0.0942149
$815$	−33.0366	−1.15722
$816$	−7.29017	−0.255207
$817$	−23.4629	−0.820862
$818$	−17.5388	−0.613230
$819$	77.1404	2.69550
$820$	−15.0384	−0.525163
$821$	−12.0561	−0.420762	−0.210381	−	0.977619i	$-0.567470\pi$
$821$	−12.0561	−0.420762	−0.210381	+	0.977619i	$0.567470\pi$
$822$	−24.1898	−0.843716
$823$	−2.06920	−0.0721279	−0.0360639	−	0.999349i	$-0.511482\pi$
$823$	−2.06920	−0.0721279	−0.0360639	+	0.999349i	$0.511482\pi$
$824$	18.6582	0.649989
$825$	−17.7404	−0.617640
$826$	2.84561	0.0990114
$827$	−53.9630	−1.87648	−0.938239	−	0.345988i	$-0.887544\pi$
$827$	−53.9630	−1.87648	−0.938239	+	0.345988i	$0.887544\pi$
$828$	10.4269	0.362358
$829$	−36.5330	−1.26884	−0.634422	−	0.772987i	$-0.718762\pi$
$829$	−36.5330	−1.26884	−0.634422	+	0.772987i	$0.718762\pi$
$830$	−18.6525	−0.647438
$831$	−16.3996	−0.568896
$832$	−5.82293	−0.201874
$833$	−28.5331	−0.988614
$834$	7.26728	0.251645
$835$	−69.0790	−2.39058
$836$	18.8629	0.652387
$837$	0.841278	0.0290788
$838$	−1.22367	−0.0422708
$839$	6.00424	0.207289	0.103645	−	0.994614i	$-0.466950\pi$
$839$	6.00424	0.207289	0.103645	+	0.994614i	$0.466950\pi$
$840$	−27.6724	−0.954788
$841$	−20.8630	−0.719412
$842$	−24.8823	−0.857500
$843$	35.1752	1.21150
$844$	19.8775	0.684212
$845$	56.5739	1.94620
$846$	−38.7203	−1.33123
$847$	6.72925	0.231220
$848$	−12.5809	−0.432032
$849$	−76.6599	−2.63096
$850$	−6.78136	−0.232599
$851$	−2.83257	−0.0970994
$852$	19.3151	0.661725
$853$	49.5840	1.69772	0.848862	−	0.528615i	$-0.177289\pi$
$853$	49.5840	1.69772	0.848862	+	0.528615i	$0.177289\pi$
$854$	−18.4269	−0.630555
$855$	−53.9777	−1.84600
$856$	9.83282	0.336079
$857$	−7.08043	−0.241863	−0.120931	−	0.992661i	$-0.538588\pi$
$857$	−7.08043	−0.241863	−0.120931	+	0.992661i	$0.538588\pi$
$858$	44.4750	1.51835
$859$	11.0460	0.376885	0.188443	−	0.982084i	$-0.439656\pi$
$859$	11.0460	0.376885	0.188443	+	0.982084i	$0.439656\pi$
$860$	10.2961	0.351095
$861$	56.8300	1.93676
$862$	11.2312	0.382536
$863$	−11.3711	−0.387077	−0.193539	−	0.981093i	$-0.561996\pi$
$863$	−11.3711	−0.387077	−0.193539	+	0.981093i	$0.561996\pi$
$864$	0.586094	0.0199393
$865$	68.2636	2.32103
$866$	16.6998	0.567481
$867$	−21.1634	−0.718746
$868$	−5.87861	−0.199533
$869$	−38.4371	−1.30389
$870$	−19.2742	−0.653457
$871$	−36.1177	−1.22380
$872$	0.101601	0.00344064
$873$	−28.2068	−0.954655
$874$	−19.8773	−0.672361
$875$	29.6715	1.00308
$876$	29.3132	0.990400
$877$	−21.1332	−0.713618	−0.356809	−	0.934177i	$-0.616135\pi$
$877$	−21.1332	−0.713618	−0.356809	+	0.934177i	$0.616135\pi$
$878$	−13.9250	−0.469946
$879$	−60.1351	−2.02831
$880$	−8.27753	−0.279036
$881$	−57.0578	−1.92233	−0.961163	−	0.275981i	$-0.910997\pi$
$881$	−57.0578	−1.92233	−0.961163	+	0.275981i	$0.910997\pi$
$882$	31.6124	1.06444
$883$	53.4996	1.80040	0.900202	−	0.435473i	$-0.143419\pi$
$883$	53.4996	1.80040	0.900202	+	0.435473i	$0.143419\pi$
$884$	17.0008	0.571800
$885$	−4.69478	−0.157813
$886$	18.8161	0.632139
$887$	−33.4807	−1.12417	−0.562086	−	0.827079i	$-0.690001\pi$
$887$	−33.4807	−1.12417	−0.562086	+	0.827079i	$0.690001\pi$
$888$	−2.19419	−0.0736322
$889$	63.7864	2.13933
$890$	24.3578	0.816475
$891$	25.2076	0.844487
$892$	0.398635	0.0133473
$893$	73.8149	2.47012
$894$	−27.6891	−0.926062
$895$	45.2435	1.51232
$896$	−4.09546	−0.136820
$897$	−46.8669	−1.56484
$898$	−14.2232	−0.474635
$899$	−4.09454	−0.136561
$900$	7.51321	0.250440
$901$	36.7318	1.22371
$902$	16.9993	0.566016
$903$	−38.9090	−1.29481
$904$	6.52342	0.216966
$905$	66.5904	2.21354
$906$	−18.6975	−0.621184
$907$	−19.9105	−0.661116	−0.330558	−	0.943786i	$-0.607237\pi$
$907$	−19.9105	−0.661116	−0.330558	+	0.943786i	$0.607237\pi$
$908$	−10.4383	−0.346406
$909$	34.3411	1.13902
$910$	64.5326	2.13924
$911$	0.0878216	0.00290966	0.00145483	−	0.999999i	$-0.499537\pi$
$911$	0.0878216	0.00290966	0.00145483	+	0.999999i	$0.499537\pi$
$912$	−15.3975	−0.509863
$913$	21.0848	0.697803
$914$	−20.4935	−0.677864
$915$	30.4013	1.00504
$916$	4.96378	0.164008
$917$	−17.5570	−0.579783
$918$	−1.71118	−0.0564775
$919$	24.5232	0.808947	0.404473	−	0.914550i	$-0.367455\pi$
$919$	24.5232	0.808947	0.404473	+	0.914550i	$0.367455\pi$
$920$	8.72269	0.287579
$921$	−34.1450	−1.12511
$922$	−39.6905	−1.30714
$923$	−45.0433	−1.48262
$924$	31.2808	1.02906
$925$	−2.04105	−0.0671093
$926$	16.6062	0.545712
$927$	60.3541	1.98229
$928$	−2.85255	−0.0936396
$929$	−8.33028	−0.273308	−0.136654	−	0.990619i	$-0.543635\pi$
$929$	−8.33028	−0.273308	−0.136654	+	0.990619i	$0.543635\pi$
$930$	9.69874	0.318034
$931$	−60.2647	−1.97509
$932$	−23.1950	−0.759778
$933$	72.0664	2.35935
$934$	27.3935	0.896341
$935$	24.1674	0.790358
$936$	−18.8356	−0.615660
$937$	−12.6635	−0.413700	−0.206850	−	0.978373i	$-0.566321\pi$
$937$	−12.6635	−0.413700	−0.206850	+	0.978373i	$0.566321\pi$
$938$	−25.4028	−0.829430
$939$	14.0422	0.458251
$940$	−32.3919	−1.05651
$941$	−6.94526	−0.226409	−0.113205	−	0.993572i	$-0.536112\pi$
$941$	−6.94526	−0.226409	−0.113205	+	0.993572i	$0.536112\pi$
$942$	7.98616	0.260203
$943$	−17.9136	−0.583346
$944$	−0.694820	−0.0226145
$945$	−6.49539	−0.211295
$946$	−11.6387	−0.378407
$947$	48.9991	1.59226	0.796128	−	0.605129i	$-0.206878\pi$
$947$	48.9991	1.59226	0.796128	+	0.605129i	$0.206878\pi$
$948$	31.3757	1.01904
$949$	−68.3590	−2.21903
$950$	−14.3229	−0.464696
$951$	78.2660	2.53795
$952$	11.9573	0.387537
$953$	−27.2406	−0.882408	−0.441204	−	0.897407i	$-0.645448\pi$
$953$	−27.2406	−0.882408	−0.441204	+	0.897407i	$0.645448\pi$
$954$	−40.6959	−1.31758
$955$	−41.3958	−1.33954
$956$	6.72223	0.217412
$957$	21.7875	0.704291
$958$	−1.87016	−0.0604222
$959$	39.6759	1.28120
$960$	6.75684	0.218076
$961$	−28.9396	−0.933537
$962$	5.11690	0.164976
$963$	31.8065	1.02495
$964$	−0.430993	−0.0138813
$965$	−54.1652	−1.74364
$966$	−32.9631	−1.06057
$967$	26.2838	0.845229	0.422615	−	0.906310i	$-0.361112\pi$
$967$	26.2838	0.845229	0.422615	+	0.906310i	$0.361112\pi$
$968$	−1.64310	−0.0528112
$969$	44.9552	1.44417
$970$	−23.5967	−0.757644
$971$	24.4929	0.786015	0.393008	−	0.919535i	$-0.371435\pi$
$971$	24.4929	0.786015	0.393008	+	0.919535i	$0.371435\pi$
$972$	−22.3349	−0.716393
$973$	−11.9197	−0.382129
$974$	42.9867	1.37738
$975$	−33.7705	−1.08152
$976$	4.49934	0.144020
$977$	−28.2896	−0.905065	−0.452532	−	0.891748i	$-0.649479\pi$
$977$	−28.2896	−0.905065	−0.452532	+	0.891748i	$0.649479\pi$
$978$	−30.4838	−0.974763
$979$	−27.5340	−0.879990
$980$	26.4457	0.844777
$981$	0.328651	0.0104930
$982$	1.83166	0.0584508
$983$	−16.9724	−0.541336	−0.270668	−	0.962673i	$-0.587244\pi$
$983$	−16.9724	−0.541336	−0.270668	+	0.962673i	$0.587244\pi$
$984$	−13.8763	−0.442361
$985$	2.01557	0.0642213
$986$	8.32842	0.265231
$987$	122.409	3.89632
$988$	35.9074	1.14237
$989$	12.2646	0.389993
$990$	−26.7755	−0.850982
$991$	50.3559	1.59961	0.799803	−	0.600262i	$-0.204937\pi$
$991$	50.3559	1.59961	0.799803	+	0.600262i	$0.204937\pi$
$992$	1.43540	0.0455739
$993$	−34.7415	−1.10249
$994$	−31.6805	−1.00484
$995$	−45.5622	−1.44442
$996$	−17.2112	−0.545358
$997$	−44.1436	−1.39804	−0.699021	−	0.715101i	$-0.746381\pi$
$997$	−44.1436	−1.39804	−0.699021	+	0.715101i	$0.746381\pi$
$998$	−3.05287	−0.0966368
$999$	−0.515031	−0.0162949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.64	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.64	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.49694 q^{3} +1.00000 q^{4} +2.70604 q^{5} +2.49694 q^{6} -4.09546 q^{7} +1.00000 q^{8} +3.23472 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.49694 q^{3} +1.00000 q^{4} +2.70604 q^{5} +2.49694 q^{6} -4.09546 q^{7} +1.00000 q^{8} +3.23472 q^{9} +2.70604 q^{10} -3.05891 q^{11} +2.49694 q^{12} -5.82293 q^{13} -4.09546 q^{14} +6.75684 q^{15} +1.00000 q^{16} -2.91964 q^{17} +3.23472 q^{18} -6.16655 q^{19} +2.70604 q^{20} -10.2261 q^{21} -3.05891 q^{22} +3.22341 q^{23} +2.49694 q^{24} +2.32267 q^{25} -5.82293 q^{26} +0.586094 q^{27} -4.09546 q^{28} -2.85255 q^{29} +6.75684 q^{30} +1.43540 q^{31} +1.00000 q^{32} -7.63791 q^{33} -2.91964 q^{34} -11.0825 q^{35} +3.23472 q^{36} -0.878750 q^{37} -6.16655 q^{38} -14.5395 q^{39} +2.70604 q^{40} -5.55733 q^{41} -10.2261 q^{42} +3.80486 q^{43} -3.05891 q^{44} +8.75331 q^{45} +3.22341 q^{46} -11.9702 q^{47} +2.49694 q^{48} +9.77283 q^{49} +2.32267 q^{50} -7.29017 q^{51} -5.82293 q^{52} -12.5809 q^{53} +0.586094 q^{54} -8.27753 q^{55} -4.09546 q^{56} -15.3975 q^{57} -2.85255 q^{58} -0.694820 q^{59} +6.75684 q^{60} +4.49934 q^{61} +1.43540 q^{62} -13.2477 q^{63} +1.00000 q^{64} -15.7571 q^{65} -7.63791 q^{66} +6.20266 q^{67} -2.91964 q^{68} +8.04868 q^{69} -11.0825 q^{70} +7.73550 q^{71} +3.23472 q^{72} +11.7396 q^{73} -0.878750 q^{74} +5.79958 q^{75} -6.16655 q^{76} +12.5276 q^{77} -14.5395 q^{78} +12.5656 q^{79} +2.70604 q^{80} -8.24073 q^{81} -5.55733 q^{82} -6.89291 q^{83} -10.2261 q^{84} -7.90067 q^{85} +3.80486 q^{86} -7.12266 q^{87} -3.05891 q^{88} +9.00125 q^{89} +8.75331 q^{90} +23.8476 q^{91} +3.22341 q^{92} +3.58410 q^{93} -11.9702 q^{94} -16.6870 q^{95} +2.49694 q^{96} -8.71999 q^{97} +9.77283 q^{98} -9.89472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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